code/recursion/finished_code/baseX.cpp

This program determines the representation of an integer in any base between 2 and 36. It could easily be extended to include higher bases, by adding to the string digits.

                
#include <iostream>
#include <string>

using namespace std;

The following string gives us up to 36 digits: just add more characters and you can handle larger bases. An obvious first move would be to add lower case letters. One could then continue with punctuation marks.

                
char digits[] = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";

Our recursive procedure is to strip a number off the back of num by modding it with the base, and then make a recursive call that processes the rest of the number, by passing in num / base.

                
string num_to_baseX(int num, int base) {
    string s;
    cout << "Converting " << num << " to base " << base << endl;
    s += digits[num % base];  // strip off from the back
    string rest;
    if (num >= base)
        rest = num_to_baseX(num / base, base);
    return rest + s;
}

int main() {
    int num, base;
    cout << "Enter a number (in base 10!) to convert: \n";
    cin >> num;
    cout << "Enter a base to convert to: \n";
    cin >> base;
    string result = num_to_baseX(num, base);
    cout << result << endl;
}